Make the dough: Combine bread flour, warm milk, sugar, instant yeast, salt, yogurt, and oil. Knead until smooth and soft, 8-10 minutes by hand or 5-6 minutes in a stand mixer. Cover and let rise until doubled, about 1 hour.
Boil potatoes: Place peeled and chopped potatoes in a pot of cold water. Bring to a boil and cook until completely fork tender, 15-20 minutes. Drain thoroughly and let steam dry.
Make the filling: Mash potatoes until completely smooth. Add mayo, butter, salt, and garlic powder and mix until creamy. Taste and adjust salt. Set aside to cool.
Portion the dough: Punch down the risen dough and divide into 6 equal pieces. Roll into smooth balls, cover, and rest for 15 minutes.
Fill: Roll each ball into a 6-7 inch circle. Layer mozzarella, potato filling, then more mozzarella in the center leaving a 1-2 inch border.
Seal: Bring edges up to the center, pleating and pinching firmly to seal with no gaps. Flip seam-side down.
Roll out: Gently flatten each stuffed ball into a circle about ½ inch thick using even pressure from the center outward.
Pan fry: Heat a non-stick pan over medium heat with a light spray of oil. Cook for 3-4 minutes per side until deeply golden brown and cheese is fully melted.
Brush with garlic butter: Brush generously with melted garlic butter while still hot.
Serve: Serve immediately while hot and melty. Repeat with remaining flatbreads.
